The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  1  X  X  1  1  X  X X^2  X  X  1  1  X X^2  X  X  1  X X^2 X^3 X^2  0  X  X X^2 X^2  X X^2 X^3 X^3  0  1 X^2 X^3  1
 0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+1x^66+28x^67+1x^68+1x^70

The gray image is a linear code over GF(2) with n=520, k=5 and d=264.
This code was found by Heurico 1.16 in 0.156 seconds.